Blast Radius Calculator

Blast effects scale with the cube root of explosive energy (Hopkinson–Cranz scaling).

How the Math Works

The Blast Radius Calculator uses cube-root scaling to estimate the radius of an explosion's destructive force. The formula R ≈ Z·W^(1/3) relates the radius (R) to the explosive yield (W), scaled by a constant (Z) that accounts for environmental factors like terrain or atmospheric conditions. The cube-root relationship arises because energy disperses in three-dimensional space, meaning doubling the yield only increases the radius by about 26%, not doubling it. This scaling law simplifies complex physics into an accessible predictive tool.

Practical Applications

To use the calculator, input the explosive yield (in kilograms of TNT equivalent) and select or input a suitable Z value based on the environment (e.g., urban vs. open terrain). The result provides an estimated radius in meters or kilometers, helping users plan safety zones, emergency response areas, or hazard assessments. For example, planners might use this to determine evacuation perimeters for industrial facilities or military operations, while engineers can design structures to withstand specific blast loads.

Day-to-Day Use

Understanding blast radii helps individuals and communities prepare for potential hazards, such as industrial accidents or natural disasters involving explosions. It also aids in interpreting news reports about large-scale incidents, allowing people to gauge risks to their safety or infrastructure. Additionally, this knowledge supports educational initiatives, helping students grasp energy dispersion principles in physics and engineering, and assists professionals in fields like urban planning or environmental science to mitigate risks proactively.

Worked example

1000 kg TNT at 35 kPa overpressure → roughly 66 m.

FAQ